再保险最优化模型分析
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摘要
本文主要在微观层面上分析了再保险研究中一个突出的问题：再保险最优化。从原保险人利用再保险转移风险的目的出发，本文集中讨论了均值方差原理、效用原理及夏普比率(风险收益比率)下的再保险最优化模型，三种原理的含义、基本思想及所适用的条件。
目前，我国已加入世界贸易组织(WTO)，距离再保险市场的完全开放仅有几年的时间。在这样的背景下，特别是在保险还远远滞后于西方发达国家的情况下，再保险的经营，尤其是科学的分保安排显得至关重要。它关系到再保险功能的有效发挥，关系到保险业的健康发展，关系到中国再保险业的国际核心竞争力。
全文共分四个部分
第一章是绪论，介绍了选题背景及意义，引出再保险最优化的问题，概述了再保险最优化方法，阐述了研究的主要内容与结构安排。第二章讨论了均值方差原理下的再保险最优化模型及其适用条件，针对停止损失再保险，得出个体模型与集合模型下的最优结论。第三章讨论了效用理论下的再保险最优化模型及适用条件，并讨论了最优策略的性质。第四章讨论了夏普比率下的再保险最优化模型及其适用条件，推出了更一般的模型。
本文的创新主要体现在下面两个方面：
1．对所收集到的资料进行系统的归纳和整理，提出了再保险最优化的定义，总结了再保险最优化的思想方法。
2．在夏普比率下的再保险最优化模型的讨论中，依据基本的优化思想，采用定量与定性分析相结合的方法，得出保险风险组合与财务风险组合下的最优化结论。
This paper primarily focuses on one issue in the field of reinsurance research: reinsurance optimization. With the perspective of risk transferring, this thesis focuses on discussing the reinsurance optimization model under mean-variance principle, utility theory and sharpe's ratio, their meanings, basic ideas and conditions applicable.
At present, China has been a member of WTO. It is not long before the fully opening up of Chinese reinsurance market. Reinsurance operation, especially the scientific arrangement of ceding business is of great importance to insurance company. It relates to reinsurance function's developing effectively, relates to insurance industry's healthy development, relates to internationally core competition ability of Chinese reinsurance industry.
This thesis consists of four chapters as the following: Chapter 1 is introduction, introduces backgrounds and meaning of theme selection, then arises out of the problem of reinsurance optimization, summarizes the methods of reinsurance optimization, expatiates on the main content and the framework. Chapter 2 discusses reinsurance optimization model under mean-variance principle. Aiming at change stop loss reinsurance, it derives optimal conclusions of both individual model and collective model. Chapter 3 discusses reinsurance optimization model under utility theory and the conditions applicable, then discusses the properties of optimal tactics. Chapter 4 discusses reinsurance optimization model under sharpe's ratio and the conditions applicable, it derives more general model.
The innovations in this thesis may be as follows:
1.Generalizing the material collected systematically, putting forward to the concept of reinsurance optimization, summarizing the theoretic approach of reinsurance optimization.
2. During the discussion of reinsurance optimization under sharpe's ratio, it derives the conclusions of optimization with the combination of insurance risk and financial risk through quantitative and qualitative analysis.
目前，我国已加入世界贸易组织(WTO)，距离再保险市场的完全开放仅有几年的时间。在这样的背景下，特别是在保险还远远滞后于西方发达国家的情况下，再保险的经营，尤其是科学的分保安排显得至关重要。它关系到再保险功能的有效发挥，关系到保险业的健康发展，关系到中国再保险业的国际核心竞争力。
全文共分四个部分
第一章是绪论，介绍了选题背景及意义，引出再保险最优化的问题，概述了再保险最优化方法，阐述了研究的主要内容与结构安排。第二章讨论了均值方差原理下的再保险最优化模型及其适用条件，针对停止损失再保险，得出个体模型与集合模型下的最优结论。第三章讨论了效用理论下的再保险最优化模型及适用条件，并讨论了最优策略的性质。第四章讨论了夏普比率下的再保险最优化模型及其适用条件，推出了更一般的模型。
本文的创新主要体现在下面两个方面：
1．对所收集到的资料进行系统的归纳和整理，提出了再保险最优化的定义，总结了再保险最优化的思想方法。
2．在夏普比率下的再保险最优化模型的讨论中，依据基本的优化思想，采用定量与定性分析相结合的方法，得出保险风险组合与财务风险组合下的最优化结论。
This paper primarily focuses on one issue in the field of reinsurance research: reinsurance optimization. With the perspective of risk transferring, this thesis focuses on discussing the reinsurance optimization model under mean-variance principle, utility theory and sharpe's ratio, their meanings, basic ideas and conditions applicable.
At present, China has been a member of WTO. It is not long before the fully opening up of Chinese reinsurance market. Reinsurance operation, especially the scientific arrangement of ceding business is of great importance to insurance company. It relates to reinsurance function's developing effectively, relates to insurance industry's healthy development, relates to internationally core competition ability of Chinese reinsurance industry.
This thesis consists of four chapters as the following: Chapter 1 is introduction, introduces backgrounds and meaning of theme selection, then arises out of the problem of reinsurance optimization, summarizes the methods of reinsurance optimization, expatiates on the main content and the framework. Chapter 2 discusses reinsurance optimization model under mean-variance principle. Aiming at change stop loss reinsurance, it derives optimal conclusions of both individual model and collective model. Chapter 3 discusses reinsurance optimization model under utility theory and the conditions applicable, then discusses the properties of optimal tactics. Chapter 4 discusses reinsurance optimization model under sharpe's ratio and the conditions applicable, it derives more general model.
The innovations in this thesis may be as follows:
1.Generalizing the material collected systematically, putting forward to the concept of reinsurance optimization, summarizing the theoretic approach of reinsurance optimization.
2. During the discussion of reinsurance optimization under sharpe's ratio, it derives the conclusions of optimization with the combination of insurance risk and financial risk through quantitative and qualitative analysis.
引文
[1] 赵正堂．巨灾保险证券化研究：[硕士学位论文]．湖南：湖南大学金融学院，2002
[2] Van Heerwaarden. A.E., Kaas,R., Goovaerts, M.J. Optimal reinsurance in relation to ordering of risks. Insurance: Mathematics & Economics, 1989,(8): 11～17
[3] Michel Denuit, Catherine Vemandele. Optimal reinsurance and stop-loss order. Insurance: Mathematics & Economics, 1998, (22): 229～233
[4] Gajek. L., Zagrodny, D. Insurer's optimal reinsurance strategies. Insurance: Mathematics & Economics, 2000, (27): 105～112
[5] [瑞士]汉斯U．盖伯．数学风险论导引．第一版．北京：世界图书出版社，1997
[6] Marek kalusza. Optimal reinsurance under mean-variance premium principles. Insurance: Mathematics & Economics, 2001, (28): 61～67
[7] Pesonen. M. Optimal reinsurance. Scandinavian Actuarial Journal, 1984, (84): 65～90
[8] H.G. Verbeek. On optimal reinsurance. Astin bulletin, 1966,4(1):29～38
[9] 谢志刚，韩天雄．风险理论与非寿险精算．第一版．天津：南开大学出版社，2000
[10] 胡宣达，沈厚才．风险管理学基础—数理方法．南京：东南大学出版社，2002
[11] 张琳，王刚．最优再保险的两类定价模型．财经理论与实践，2003，24(123)：24～26
[12] Borch. K.H. Economics of insurance. Amsterdan: North—Holland, 1990
[13] Karl Borch. The optimal reinsurance treaty. Astin Bulletin, 1969,5(2): 284～290
[14] 汪端阳，李伯经．效用理论在再保险中的应用．经济数学，1999，(2)：53～56
[15] Martina Vandebroer. Pareto optimal and profit-sharing. Astin Bulletin, 1998, 18(1):47-55
[16] 博迪，凯恩，马库斯．投资学．第四版．北京：机械工业出版社，1999
[17] Rene Schnieper. Portfolio optimization. Astin Bulletin, 2000, 30(1): 195～202
[18] Arrow, K. J. Optimal insurance and generalized deductibles. Scandinavian
Actuarial Journal, 1974,8(1): 1～42
[19] Aumann, R., M.Maschler. The bargaining set for cooperative games annuals of mathematical Studies. 1964, (52): 443～476
[20] Karl Borch. An attempt to determine the optimum amount of stop loss reinsurance. Transaction of the 16th international congress of Actuaries, 1960,1(3): 579～610
[21] Karl Borch. Reciprocal reinsurance treaties. Astin Bulletin, 1960,1(4): 170～191
[22] R.KAAS, Van Herwarden. On stop-loss premiums for the individual model. Astin Bulletin, 1998,18(1): 91～97
[23] 方春银．试析影响再保险业务定价的因素．保险研究，1999，(12)：19～22
[24] 胡炳志．再保险．第一版．北京：中国金融出版社，1998
[25] 曾松百．两类新型再保险产品的特性与定价分析：[硕士学位论文]．湖南：湖南大学金融学院，2002
[26] 项宇，谢志刚．中国再保险市场供求状况分析．财经研究，2000，(8)：59～64
[27] 方春银．超额再保险定价分析．保险研究，2002，(5)：19～20
[28] 王勇．再保险安排中危险单位与保险单的分离．保险研究，2002，(6)：47～49
[29] Karl Borch. The utility concept applied to the theory of insurance. Astin Bulletin, 1961,1(5): 245～255
[30] Jaquette, S.C. Utility Criteria for Markov decision processes. Management Science, 1976
[31] 左吉贵．谈再保险分出比例对公司利润的影响．山西财经大学学报，2001，(2)：58
[32] 成显赫．谈谈再保险业务自留额的确定．保险研究，1999，(7)：30，35～36
[33] Ohlin, J. On a class of measures of dispersion with application to optimal reinsurance. Astin Bulletin, 1996,26 (2): 249～266
[34] 徐光辉，刘彦佩，程侃．运筹学基础手册．北京：科学出版社，2002
[35] Kahn, P.M. Some remarks on a recent paper by Borch. Astin Bulletin, 1957, 1 (2): 265～272
[36] 张维迎．博弈论与信息经济学．第一版．上海：上海人民出版社，1996
[37] Borch, K. Equilibrium in a reinsurance market. Econometrica, 1962,(30):424～
444
[38] Vajda, S. Minimum variance reinsurance. Astin Bulletin, 1962,2(2): 257～260
[39] 容喜民，张世英．再保险定价的研究．系统工程学报，2001，(6)：31～33
[40] 张瑞，臧振春，张新祥．效用理论在保险中的应用．经济经纬，2000，(3)：39～41
[41] Karl Borch. The economics of uncertainty. Princeton University Press, 1968
[2] Van Heerwaarden. A.E., Kaas,R., Goovaerts, M.J. Optimal reinsurance in relation to ordering of risks. Insurance: Mathematics & Economics, 1989,(8): 11～17
[3] Michel Denuit, Catherine Vemandele. Optimal reinsurance and stop-loss order. Insurance: Mathematics & Economics, 1998, (22): 229～233
[4] Gajek. L., Zagrodny, D. Insurer's optimal reinsurance strategies. Insurance: Mathematics & Economics, 2000, (27): 105～112
[5] [瑞士]汉斯U．盖伯．数学风险论导引．第一版．北京：世界图书出版社，1997
[6] Marek kalusza. Optimal reinsurance under mean-variance premium principles. Insurance: Mathematics & Economics, 2001, (28): 61～67
[7] Pesonen. M. Optimal reinsurance. Scandinavian Actuarial Journal, 1984, (84): 65～90
[8] H.G. Verbeek. On optimal reinsurance. Astin bulletin, 1966,4(1):29～38
[9] 谢志刚，韩天雄．风险理论与非寿险精算．第一版．天津：南开大学出版社，2000
[10] 胡宣达，沈厚才．风险管理学基础—数理方法．南京：东南大学出版社，2002
[11] 张琳，王刚．最优再保险的两类定价模型．财经理论与实践，2003，24(123)：24～26
[12] Borch. K.H. Economics of insurance. Amsterdan: North—Holland, 1990
[13] Karl Borch. The optimal reinsurance treaty. Astin Bulletin, 1969,5(2): 284～290
[14] 汪端阳，李伯经．效用理论在再保险中的应用．经济数学，1999，(2)：53～56
[15] Martina Vandebroer. Pareto optimal and profit-sharing. Astin Bulletin, 1998, 18(1):47-55
[16] 博迪，凯恩，马库斯．投资学．第四版．北京：机械工业出版社，1999
[17] Rene Schnieper. Portfolio optimization. Astin Bulletin, 2000, 30(1): 195～202
[18] Arrow, K. J. Optimal insurance and generalized deductibles. Scandinavian
Actuarial Journal, 1974,8(1): 1～42
[19] Aumann, R., M.Maschler. The bargaining set for cooperative games annuals of mathematical Studies. 1964, (52): 443～476
[20] Karl Borch. An attempt to determine the optimum amount of stop loss reinsurance. Transaction of the 16th international congress of Actuaries, 1960,1(3): 579～610
[21] Karl Borch. Reciprocal reinsurance treaties. Astin Bulletin, 1960,1(4): 170～191
[22] R.KAAS, Van Herwarden. On stop-loss premiums for the individual model. Astin Bulletin, 1998,18(1): 91～97
[23] 方春银．试析影响再保险业务定价的因素．保险研究，1999，(12)：19～22
[24] 胡炳志．再保险．第一版．北京：中国金融出版社，1998
[25] 曾松百．两类新型再保险产品的特性与定价分析：[硕士学位论文]．湖南：湖南大学金融学院，2002
[26] 项宇，谢志刚．中国再保险市场供求状况分析．财经研究，2000，(8)：59～64
[27] 方春银．超额再保险定价分析．保险研究，2002，(5)：19～20
[28] 王勇．再保险安排中危险单位与保险单的分离．保险研究，2002，(6)：47～49
[29] Karl Borch. The utility concept applied to the theory of insurance. Astin Bulletin, 1961,1(5): 245～255
[30] Jaquette, S.C. Utility Criteria for Markov decision processes. Management Science, 1976
[31] 左吉贵．谈再保险分出比例对公司利润的影响．山西财经大学学报，2001，(2)：58
[32] 成显赫．谈谈再保险业务自留额的确定．保险研究，1999，(7)：30，35～36
[33] Ohlin, J. On a class of measures of dispersion with application to optimal reinsurance. Astin Bulletin, 1996,26 (2): 249～266
[34] 徐光辉，刘彦佩，程侃．运筹学基础手册．北京：科学出版社，2002
[35] Kahn, P.M. Some remarks on a recent paper by Borch. Astin Bulletin, 1957, 1 (2): 265～272
[36] 张维迎．博弈论与信息经济学．第一版．上海：上海人民出版社，1996
[37] Borch, K. Equilibrium in a reinsurance market. Econometrica, 1962,(30):424～
444
[38] Vajda, S. Minimum variance reinsurance. Astin Bulletin, 1962,2(2): 257～260
[39] 容喜民，张世英．再保险定价的研究．系统工程学报，2001，(6)：31～33
[40] 张瑞，臧振春，张新祥．效用理论在保险中的应用．经济经纬，2000，(3)：39～41
[41] Karl Borch. The economics of uncertainty. Princeton University Press, 1968